# World Football Elo Ratings

The World Football Elo Ratings is a ranking system for men's national teams in association football. The method used to rank teams is based upon the Elo rating system method but modified to take various football-specific variables into account. These ratings should not be confused with the FIFA World Rankings, which is more prevalent because it is the official rating system used by the international governing body of football to rank national teams.

The ratings consider all international "A" matches for which results could be found. Ratings tend to converge on a team's true strength relative to its competitors after about 30 matches.[1] Ratings for teams with fewer than 30 matches should be considered provisional.

The FIFA Women's World Rankings system uses a modified version of the Elo formula whereas the FIFA men's ranking system uses a non-Elo formula.

## Top 60 ranking

Current table, as of 9 March 2014, of the World Football Elo Ratings, compiled by the World Football Elo Ratings web site.

Each national team's FIFA World Rankings as of 13 February 2014.[2] Cell color indicates confederation.

Elo Rank Team Points Confederation FIFA Rank
1  Brazil 2113 CONMEBOL 9
2  Spain 2086 UEFA 1
3  Germany 2064 UEFA 2
4  Argentina 1989 CONMEBOL 3
5  Netherlands 1963 UEFA 10
6  England 1909 UEFA 15
7  Portugal 1908 UEFA 4
8  Colombia 1904 CONMEBOL 5
9  Uruguay 1894 CONMEBOL 7
10  Chile 1892 CONMEBOL 14
11  Italy 1885 UEFA 8
12  France 1872 UEFA 18
13  United States 1829 CONCACAF 13
15  Russia 1822 UEFA 22
16   Switzerland 1819 UEFA 6
17  Ukraine 1814 UEFA 18
18  Belgium 1805 UEFA 11
19  Mexico 1795 CONCACAF 21
Sweden 1795 UEFA 25
21  Greece 1790 UEFA 12
22  Ivory Coast 1789 CAF 23
23  Croatia 1784 UEFA 16
24  Japan 1752 AFC 50
25  Bosnia and Herzegovina 1740 UEFA 17
Serbia 1740 UEFA 29
27  Czech Republic 1727 UEFA 31
28  Denmark 1726 UEFA 20
29  Nigeria 1720 CAF 47
30  Egypt 1713 CAF 38
Elo Rank Team Points Confederation FIFA Rank
31  Iran 1709 AFC 38
32  Costa Rica 1707 CONCACAF 35
33  Australia 1705 AFC 53
34  Turkey 1698 UEFA 42
35  Peru 1696 CONMEBOL 41
36  South Korea 1690 AFC 61
37  Ghana 1689 CAF 37
38  Romania 1686 UEFA 33
39  Panama 1683 CONCACAF 32
Scotland 1683 UEFA 34
41  Venezuela 1677 CONMEBOL 35
42  Republic of Ireland 1675 UEFA 67
43  Paraguay 1674 CONMEBOL 49
44  Honduras 1673 CONCACAF 40
45  Finland 1659 UEFA 65
46  United Arab Emirates 1647 AFC 58
47  Austria 1643 UEFA 43
48  Hungary 1637 UEFA 44
49  Uzbekistan 1634 AFC 57
50  Slovenia 1620 UEFA 27
51  Bulgaria 1619 UEFA 72
52  Poland 1616 UEFA 70
53  Bolivia 1603 CONMEBOL 70
54  Slovakia 1601 UEFA 54
55  Israel 1597 UEFA 56
56  Algeria 1595 CAF 26
57  Norway 1593 UEFA 60
58  Cameroon 1590 CAF 46
59  South Africa 1582 CAF 64
60  Montenegro 1577 UEFA 52

## Strongest teams since the mid to late 1960s

Time averaged Elo or Elo-like scores are routinely used to compare chess player strengths.[3][4][5] The following is a list of the national teams with the highest average Elo score from 1 January 1970 to 1 February 2014. Before this time intercontinental play was fairly limited and many nations in Africa, North America, and Asia had played too few games yet to create a representative Elo score. Since Elo scores reflect past accomplishments, the table represents the relative strength of national teams since the mid to late 1960s.

Rank Country Avg Elo
1  Brazil 2012.5
2  (West) Germany[6] 1975.6
3  Netherlands 1924.5
4  Italy 1923.4
5  England 1922.9
6  Spain 1909.3
7  Argentina 1902.3
8  France 1881.4
9  Soviet Union → Russia[7] 1852.7
10  Czechoslovakia/Czechia[8] 1832.7
11  Portugal 1817.3
12  Yugoslavia → Serbia[9] 1817.2
13  Sweden 1798.9
14  Romania 1781.5
15  Mexico 1774.6
16  Poland 1772.9
17  Uruguay 1771.8
18  Belgium 1761.3
Rank Country Avg Elo
19  Denmark 1757.0
20  Scotland 1739.1
21  Paraguay 1727.1
22  Republic of Ireland 1720.9
23  Chile 1716.7
24  Bulgaria 1709.0
25  Australia 1696.4
26  Austria 1688.9
27  Hungary 1685.9
Switzerland 1685.9
29  Colombia 1682.0
30  Iran 1676.1
31  South Korea 1666.3
32  Greece 1655.3
33  Egypt 1654.3
34  Nigeria 1654.1
35  Wales 1654.0
Rank Country Avg Elo
36  Morocco 1645.2
37  Israel 1644.4
38  Peru 1644.0
39  Cameroon 1638.2
40  Ivory Coast 1637.8
41  Norway 1637.4
42  Turkey 1634.0
43  Ghana 1611.6
44  Northern Ireland 1608.8
45  Tunisia 1603.1
United States 1603.1
47  Costa Rica 1596.2
48  Iraq 1595.6
49  Japan 1590.0
51  Algeria 1569.6
52  Zambia 1561.0

## List of number one teams

The following is the list of nations who have achieved the number one position on the World Football Elo Ratings since 2000:

Start Date Nation # of days
5 Jun 1999  Brazil 389
28 Jun 2000  France 708
6 Jun 2002  Argentina 1
7 Jun 2002  France 4
11 Jun 2002  Netherlands 1
12 Jun 2002  Spain 4
16 Jun 2002  Netherlands 5
21 Jun 2002  Brazil 351
7 Jun 2003  Netherlands 4
11 Jun 2003  Brazil 8
19 Jun 2003  Netherlands 83
10 Sep 2003  France 291
27 Jun 2004  Czech Republic 4
1 Jul 2004  France 10
Start Date Nation # of days
11 Jul 2004  Brazil 3
14 Jul 2004  France 35
18 Aug 2004  Argentina 290
4 Jun 2005  Czech Republic 4
8 Jun 2005  Argentina 21
29 Jun 2005  Brazil 102
9 Oct 2005  Netherlands 3
12 Oct 2005  Brazil 265
4 Jul 2006  Italy 43
16 Aug 2006  France 52
7 Oct 2006  Brazil 122
6 Feb 2007  France 1
7 Feb 2007  Brazil 140
Start Date Nation # of days
27 Jun 2007  France 14
11 Jul 2007  Argentina 4
15 Jul 2007  Brazil 334
13 Jun 2008  Brazil /  Netherlands 2
15 Jun 2008  Netherlands 6
21 Jun 2008  Spain 368
24 Jun 2009  Brazil 373
2 Jul 2010  Netherlands 1
3 Jul 2010  Netherlands /  Spain 3
6 Jul 2010  Netherlands 1
7 Jul 2010  Spain 1089
30 Jun 2013  Brazil 45
14 Aug 2013  Spain 59
12 Oct 2013  Brazil 150

## Ranking by days as leader since 1 January 2000

Nation # of days Last Date as Leader
Brazil 2204 Current
Spain 1523 12 October 2013
France 1115 10 July 2007
Argentina 316 14 July 2007
Netherlands 109 6 July 2010
Italy 43 15 August 2006
Czech Republic 8 7 June 2005

## All-time highest ratings

The following is a list of national football teams ranked by their highest Elo score ever reached.

Rank Nation Points Date
1  Hungary 2166 30 June 1954
2  Brazil 2153 17 June 1962
3  Spain 2143 23 June 2013
4  Argentina 2117 3 April 1957
5  France 2106 15 August 2001
6  Netherlands 2101 6 July 2010
7  Germany 2099 4 September 1974 (as West Germany)
8  Italy 2079 20 July 1939
9  Poland 2047 1 September 1974
10  England 2041 22 October 1966
11  Uruguay 2035 13 June 1928
12  Russia 2023 9 October 1983 (as Soviet Union)
13  Czech Republic 1999 27 June 2004
14  Austria 1998 31 May 1934
15  Portugal 1983 15 November 2000
16  Croatia 1967 11 July 1998
17  Serbia 1961 25 June 1998 (as FR Yugoslavia)
18  Denmark 1960 13 June 1986
19  Scotland 1953 10 March 1888
20  Sweden 1950 25 June 1950
East Germany 1950 22 June 1974
22  Mexico 1936 19 June 2005
23  Paraguay 1932 21 February 1954
24  Chile 1919 12 July 2011
25  Belgium 1916 9 September 1981
Rank Nation Points Date
26  Norway 1913 13 June 2000
27  Colombia 1912 5 June 1994
28  Romania 1909 9 June 1990
29  Greece 1896 18 August 2004
30  Republic of Ireland 1889 21 August 2002
31  Ivory Coast 1881 26 January 2013
32   Switzerland 1876 22 June 1994
33  United States 1871 8 July 2009
34  Australia 1867 14 December 1997
Japan 1867 15 August 2001
Turkey 1867 19 June 2003
37  Ecuador 1862 26 March 2013
38  Wales 1859 20 May 1981
39  Bulgaria 1856 15 June 1969
Peru 1856 11 June 1978
41  Cameroon 1849 26 June 2003
42  Egypt 1835 31 January 2010
43  Iran 1824 8 June 2005
44  Ukraine 1820 15 November 2013
45  South Korea 1818 22 June 2002
46  Nigeria 1816 5 June 2004
47  Northern Ireland 1809 23 April 1986
48  Senegal 1803 16 June 2002
49  Costa Rica 1800 10 March 1960
50  Ghana 1799 3 February 2008

The table below shows the teams with the best average Elo score per decade (Jan 1 19X0 - Dec 31 19X9). Because the Elö scores take into account past achievements with an inercy of months, the averaging over a decade is more representative of the teams' strengths for a decade starting a few years earlier and ending with the latest results of the decade relatively underweighted. For instance, this partially explains England claiming #3 spot despite missing two WCs in the 70s, boosted by results legacy from the late 60s. Or conversely the surging of France in the late 90s and Spain in the late 00s not being fully reflected in that decade but rather on the subsequent one.

Rank 1920s 1930s 1940s 1950s 1960s
1 1911 1976 2036 2025 1962
2 1873 1970 2018 1997 1928
3 1859 1899 1892 1996 1924
4 1843 1868 1876 1917 1923
5 1820 1866 1858 1870 1917
6 1795 1859 1852 1856 1887
7 1771 1841 1841 1853 1867
8 1768 1814 1832 1850 1852
9 1761 1810 1814 1817 1843
10 1760 1785 1768 1815 1840
11 1739 1759 1766 1799 1810
12 1712 1685 1746 1796 1800
13 1734 1790 1796
14 1753 1783
15 1728 1741

Rank 1970s 1980s 1990s 2000s 2010s [10]
1 2060 1975 1998 1998 2103
2 2040 1964 1988 1984 2059
3 1948 1951 1952 1966 2024
4 1933 1927 1928 1964 2021
5 1888 1897 1920 1955 1948
6 1883 1890 1904 1941 1923
7 1877 1884 1901 1916 1877
8 1869 1884 1901 1891 1872
9 1861 1847 1869 1887 1869
10 1851 1839 1869 1872 1855
11 1838 1820 1842 1838 1853
12 1831 1819 1834 1825 1844
13 1830 1818 1828 1821 1823
14 1809 1803 1825 1807 1819
15 1803 1785 1825 1799 1816
16 1793 1784 1813 1790 1798
17 1771 1784 1810 1786 1794
18 1766 1776 1784 1785 1774
19 1766 1775 1776 1782 1766
20 1755 1773 1773 1774 1761

## Highest rated matches

A list of the 10 matches between teams with the highest combined Elo ratings (the nation's points before the matches are given).

Rank Combined
points
Nation 1 Elo 1 Nation 2 Elo 2 Score Date Occasion Location
1 4212  Netherlands 2101  Spain 2111 0 : 1 aet 2010-07-10 World Cup F Johannesburg
2 4190  Brazil 2063  Spain 2127 3 : 0 2013-06-30 Confederations Cup F Rio de Janeiro
3 4161  West Germany 1995  Hungary 2166 3 : 2 1954-07-04 World Cup F Bern
4 4159  Netherlands 2051  Brazil 2108 2 : 1 2010-07-02 World Cup QF Port Elizabeth
5 4151  Brazil 2061  Netherlands 2090 0 : 0 2011-06-04 Friendly Goiânia
6 4149  West Germany 2068  Brazil 2081 0 : 1 1973-06-16 Friendly Berlin
7 4129  Spain 2085  Germany 2044 1 : 0 2010-07-07 World Cup SF Durban
8 4120  Brazil 2051  West Germany 2069 1 : 0 1982-03-21 Friendly Rio de Janeiro
9 4118  Hungary 2108  Brazil 2010 4 : 2 1954-06-27 World Cup QF Bern
10 4116  Hungary 2141  Uruguay 1975 4 : 2 1954-06-30 World Cup SF Lausanne

## History

This system, developed by Hungarian-American mathematician Dr. Árpád Élő, is used by FIDE, the international chess federation, to rate chess players, and by the European Go Federation, to rate Go players. In 1997 Bob Runyan adapted the Elo rating system to international football and posted the results on the Internet. He was also the first maintainer of the World Football Elo Ratings web site, now maintained by Kirill Bulygin.

## Overview

The Elo system was adapted for football by adding a weighting for the kind of match, an adjustment for the home team advantage, and an adjustment for goal difference in the match result.

The factors taken into consideration when calculating a team's new rating are:

• The team's old rating
• The considered weight of the tournament
• The goal difference of the match
• The result of the match
• The expected result of the match

The different weights of competitions in descending order are:

The single difference is Elo giving a special treatment for minor tournaments, while FIFA consider them as friendly matches.

These ratings take into account all international "A" matches for which results could be found. Ratings tend to converge on a team's true strength relative to its competitors after about 30 matches. Ratings for teams with fewer than 30 matches should be considered provisional. Match data are primarily from International Football 1872 – present web site.

## Basic calculation principles

The basic principle behind the Elo ratings is only in its simplest form similar to that of a league, unlike the FIFA tables who effectively run their table as a normal league table, but with weightings to take into account the other factors, the Elo system has its one formula which takes into account the factors mentioned above. There is no first step as in the FIFA system where a team immediately receives points for the result, there is just one calculation in the Elo system.

The ratings are based on the following formulae:

$R_n = R_o + K G (W - W_e)$

or

$P = K G (W - W_e)$

Where;

 $R_n$ = The new team rating $R_o$ = The old team rating $K$ = Weight index regarding the tournament of the match $G$ = A number from the index of goal differences $W$ = The result of the match $W_e$ = The expected result $P$ = Points Change

### Status of match

The status of the match is incorporated by the use of a weight constant. The weight is a constant regarding the "weight" or importance of a match, defined by which tournament the match is in, they are as follows;

Tournament or Match type Index (K)
World Cup Finals 60
Continental Championship and Intercontinental Tournaments 50
World Cup and Continental qualifiers and major tournaments 40
All other tournaments 30
Friendly Matches 20

### Number of goals

The number of goals is taken into account by use of a goal difference index. G is increased by half if a game is won by two goals, and if the game is won by three or more goals by a number decided through the appropriate calculation shown below;

If the game is a draw or is won by one goal

$G = 1$

If the game is won by two goals

$G = \frac{3}{2}$

If the game is won by three or more goals

• Where N is the goal difference
$G = \frac{11+N}{8}$

Table of examples:

Goal Difference Coefficient of K (G)
0 1
+1 1
+2 1.5
+3 1.75
+4 1.875
+5 2
+6 2.125
+7 2.25
+8 2.375
+9 2.5
+10 2.625

### Result of match

W is the result of the game (1 for a win, 0.5 for a draw, and 0 for a loss).

### Expected result of match

We is the expected result (win expectancy with a draw counting as 0.5) from the following formula:

$W_e = \frac{1}{10^{-dr/400} + 1}$

where dr equals the difference in ratings plus 100 points for a team playing at home. So dr of 0 gives 0.5, of 120 gives 0.666 to the higher-ranked team and 0.334 to the lower, and of 800 gives 0.99 to the higher-ranked team and 0.01 to the lower.

### Examples

The same examples have been used on the FIFA World Rankings for a fair comparison. Some actual examples should help to make the methods of calculation clear. In this instance it is assumed that three teams of different strengths are involved in a small friendly tournament on neutral territory.

Before the tournament the three teams have the following point totals.

Team Points
A 630
B 500
C 480

Thus, team A is by some distance the highest ranked of the three: The following table shows the points allocations based on three possible outcomes of the match between the strongest team A, and the somewhat weaker team B:

#### Example 1

Team A versus Team B (Team A stronger than Team B)

 Score $K$ $G$ $W$ $W_e$ Total (P) Team A Team B Team A Team B Team A Team B 3 : 1 1 : 3 2 : 2 20 20 20 20 20 20 1.5 1.5 1.5 1.5 1 1 1 0 0 1 0.5 0.5 0.679 0.321 0.679 0.321 0.679 0.321 +9.63 -9.63 -20.37 +20.37 -3.58 +3.58

#### Example 2

Team B versus Team C (both teams approximately the same strength)

When the difference in strength between the two teams is less, so also will be the difference in points allocation. The following table illustrates how the points would be divided following the same results as above, but with two roughly equally ranked teams, B and C, being involved:

 Score $K$ $G$ $W$ $W_e$ Total (P) Team B Team C Team B Team C Team B Team C 3 : 1 1 : 3 2 : 2 20 20 20 20 20 20 1.5 1.5 1.5 1.5 1 1 1 0 0 1 0.5 0.5 0.529 0.471 0.529 0.471 0.529 0.471 +14.13 -14.13 -15.87 +15.87 -0.58 +0.58

Note that Team B loses more ranking points by losing to Team C than by losing to Team A.

## Notes

1. ^ "The World Football Elo Rating System". Eloratings.net. Retrieved 26 February 2012.
2. ^ "FIFA/Coca-Cola World Ranking" (Press release). FIFA. 16 January 2014. Retrieved 9 March 2014.
3. ^ Arpad E. Elo, The Rating of Chessplayers, Past and Present, Arco, 1978. ISBN 0-668-04721-6.
4. ^ Arpad Elo, Chess Life, 1962.
5. ^ About the Chessmetrics Rating System, by Jeff Sonas
6. ^ Representing West Germany from 1949 to 1990
7. ^ Combined record of the USSR (1970-1992), the CIS (1992), and Russia national football teams (1992-present)
8. ^ Combined record of Czechoslovakia (1970-1992) and Czech national football teams (1993-present)
9. ^ Combined record of Yugoslavia (1970-1992), Serbia and Montenegro (1994-2006) and Serbia national football teams (2006-present)
10. ^ (up to March 1st, 2014)
11. ^ Combined record of Yugoslavia (1990-1992) and FR of Yugoslavia (1994-1999)
12. ^ Combined record of Czechoslovakia (1990-1992) and Czech national football teams (1993-1999)
13. ^ Combined record of the USSR (1990-1992), the CIS (1992), and Russia national football teams (1992-1999)